Cancer Treatment Using Multiple Chemotheraputic Agents Subject to Drug Resistance
|
|
- Derrick Lewis
- 6 years ago
- Views:
Transcription
1 Cancer Treatment Using Multiple Chemotheraputic Agents Subject to Drug Resistance J. J. Westman Department of Mathematics University of California Box Los Angeles, CA B. R. Fabijonas Department of Mathematics Southern Methodist University P.O. Box Dallas, TX D. L. Kern Institute for Mathematics and Its Applications University of Minnesota Minneapolis, MN F. B. Hanson Laboratory for Advanced Computing M/C 249 University of Illinois at Chicago Chicago, IL Abstract A compartment model for the evolution of cancer subject to multiple chemotherapeutic agents is presented. The formulation accounts for the heterogeneous nature of cancer and drug resistance, leading to a system that can be used as a tool for optimizing treatments. Chemotherapeutic or cytotoxic agents have limited effectiveness due to of toxicity and the development of drug resistance. Toxicity limits the amount of the agent that can be used and acts as an upper bound on the dosage. Drug resistance causes the clinical value of the cytotoxic agent to become nominal after a small number of treatments. Therefore, several non-cross resistant cytotoxic agents are used to extend the number of treatments that can be administered. 1 Introduction One of the most challenging aspects of treating cancer with chemotherapy is the development of resistance to the cytotoxic agents. Drug resistance, whether intrinsic or acquired, ultimately leads 1
2 to the ineffectiveness of the agent where there is nominal clinical benefit compared to the side effects of the treatment. To counter the development of the resistance, other treatment modes or options are used that destroy the resistant and sensitive cells. The use of multimode treatments, for example chemotherapy and radiotherapy, leads to a more effective treatment plan. One of these multimode options is to use another cytotoxic agent that utilizes a different mechanism to destroy the cells and therefore should not be cross resistant, i.e., cells should not share all of the same drug resistance mechanisms. Treatment therapies utilizing multiple cytotoxic agents are commonly used in practice, see for example [1, 2, 3]. This paper extends the four compartment model presented in [4] for the evolution of cancer subjected to chemotherapy to account for the use of multiple cytotoxic agents. For concreteness, we examine the case of two non-cross resistant cytotoxic agents (say agents A and B which yields an eight compartment model. This can be extended rather easily to M non-cross resistant cytotoxic agents, where the number of compartments would be given by 2 ( M i=0 M i = 2 M+1. The resulting set of ordinary differential equations is viewed as a system which describes the evolution of the compartment populations. For the sake of brevity, the reader is referred to [4] for model details. 2 Compartmental Model Cancer can be viewed as a system consisting of three types of cells: proliferating, clonogenic and end cells. The division is based on the cells function. The first type is the proliferating fraction, which consists of cells that are currently undergoing cell division and represents the mechanism by which the cancer grows and spreads. During the cell life cycle, a number of checkpoints exist to ensure that the resulting daughter cells will be viable after mitosis. For each viable daughter cell, there exists a positive probability for the daughter cell to become any one of the three types of cells. The quiescent or clonogenic fraction consists of stem cells that are capable of propagating the cancer but are currently inactive. Given a proper stimulus, the cells in the clonogenic fraction can be recruited into the other two groups. The final type are the end cells which consists of necrotic tissue and terminally differentiated somatic tissues such as vascular structures which can support but not propagate the cancer. The goal of most treatments is to move all of the cells from the growth and clonogenic fractions into the end compartment. The end cells are not accounted for in this model since they cannot generate new cancerous cells. Drug resistance can either be intrinsic or acquired. Intrinsic resistance is resistance that exists prior to treatment. Acquired resistance to a cytotoxic agent evolves as a result of treatment with the cytotoxic agent and develops after mitosis, randomly providing the cell with mechanisms to defeat the actions of cytotoxic agents via mutations. Mutations can only occur in cells that are actively dividing, therefore only cells in the proliferating fraction can mutate. Either kind of drug resistance is assumed to be inherited by the daughter cells and their progeny. Note that resistance to a particular drug normally implies that resistance should exist for all drugs in the same category that act with the same mechanism. Thus, two drugs which use the same mechanism to attack the 2
3 cancerous cell are referred to as cross resistant. A treatment consists of administering both agents at specified times. For example, a typical treatment period is 28 days with agent A administered on day 1 and agent B on day 14. A treatment cycle consists of n treatments, and at most m cycles can be administered. Therefore a total of N = n m treatments may be given. Regimens for treatment normally start with a single treatment cycle and continue until the patient goes into remission or all of the available treatments have been administered. Upon recurrence of the cancer, a new treatment cycle begins provided a treatment is available. Figure 1 represents the eight compartment model for the evolution of heterogeneous cancer with treatment. In the figure, the solid lines represent the evolutionary dynamics of the cancer and the the dashed lines show the effects of treatments. 2.1 Mathematical Model Cancer is a stochastic evolutionary process for the various types of cells. The physical process for the development of cancer is an intractable problem since all cells and their evolution would need to be followed. Therefore, the mathematical model presented here is based on macroscopic or bulk actions and is not necessarily related to the biological processes of the individual cancerous cells. However, the bulk dynamics may be observed through means such as clinical in vitro trials or in vivo methods such as imaging. Define the unit dose impulse function, j,k (t for the time t = t j,k at which a treatment j of cytotoxic agent X k is administered by j,k (t = { 1 t = t j,k 0 otherwise where X 1 = A and X 2 = B. Define the indicator set }, (2.1 I { 0, 1, 2, 3} (2.2 to represent the classification of the cells and their resistance to the cytotoxic agents, where P i (t and C i (t for i I denote the number of cells in the proliferating and clonogenic fractions, respectively, where the index i denotes no resistance if i = 0, resistance to agent A if i = 1, resistance to agent B if i = 2, resistance to both agents if i = 3. The model that is generated predicts the evolution of the cancer starting from a single cell. Let time t = 0 be the time of the appearance of the first malignant cell from which a colony will form. This first cell must be in the growth fraction, which yields the initial conditions for the model as P 0 (0 = 1, P i (0 = 0 for i = 1, 2, 3, C i (0 = 0 for i I. (2.3 For the remainder of this section let i, s I be the indicator for the drug resistance, X k {A, B} be the cytotoxic agent administered, Y {P, C} represent proliferating or clonogenic fraction, and j = 1, 2,..., N denote the treatment number. The overall growth dynamics for the untreated cancer is assumed to be Gompertzian in nature with relative rate of change form ( K f(p 0, P 1, P 2, P 3, C 0, C 1, C 2, C 3 = λ log, (2.4 P 0 + P 1 + P 2 + P 3 + C 0 + C 1 + C 2 + C 3 3
4 P3 C3 P2 C2 P1 C1 P0 C0 Mutations due to instrinsic resistance, both gain and loss Self proliferation Natural proliferating to clonogenic migration Natural clonogenic to proliferating back migration Natural cross compartment mutations Natural cell loss to end cell compartment Acquired resistance to agent A Acquired resistance to agent B Stimulated back migration Cell loss due to agent A Cell loss due to agent B Figure 1: Schematic representation of the eight compartmental model subject to chemotherapy with cytotoxic agents A and B. The dashed lines are chemotherapy terms. Compartments to the left of the figure s center denote the proliferating compartments P i, and similarly, those on the right denote the clonogenic compartments C i, for i = 0, 1, 2, 3. Compartments aligned in rows are susceptible to neither agent (P 0, C 0, to agent A only (P 1, C 1, to agent B only (P 2, C 2, or both cytotoxic agents (P 3, C 3. 4
5 where the time dependence of P i (t and C i (t has been suppressed. The evolutionary rates for the growth of the cancer are α i denoting natural migration of daughter cells after mitosis from the proliferating to the clonogenic fraction, β i the natural back migration of clonogenic cells which restart the cell life cycle, and δ P,i or δ C,i the natural loss of cells either from the proliferating or clonogenic compartments to the end cell compartment. All of these rates are, in general, functions of (P 0, P 1, P 2, P 3, C 0, C 1, C 2, C 3, t. The probabilistic mutation rates for the viable mutated cells are denoted by µ Yi,Ys, where Y i is the compartment for the parent cell and Y s is the compartment of the daughter cell. All possible mutations are allowed, except for those mutations that have zero probability of occurring. Transitions from mutations are not allowed to stay in the same compartment, therefore µ Yi,Y i 0, and mutations are not allowed where resistance to one agent is lost and the resistance to the other is gained, therefore µ Y1,Y 2 0 and µ Y2,Y 1 0. Let j,k κ Yi,j,k denote the loss of cells in the Y i compartment due to treatment j of agent X k. A feature of this model is that only susceptible cells to a given agent X k are killed by the administration of the treatment, which is assumed to be uniform. However, the kill rates can vary to account for semi-cross resistance of cytotoxic agents. For the model in Figure 1, the nonzero kill rates are j,k κ P0,j,k, j,2 κ P1,j,2, and j,1 κ P2,j,1. As a result of the large numbers of cells killed by the administration of cytotoxic agent X k, a stimulus is generated that recruits cells form the clonogenic fraction into the proliferating fraction to ensure the viability of the cancer at rate j,k γ Ci,Y i,j,k. Side effects of treatment include the development acquired resistance at a rate j,k µ Yi,Ys,j,k. It is assumed, without loss of generality, that those cells that acquire resistance stay in the proliferating fraction. The only nonzero rates for the development of acquired resistance are j,1 µ P0,P 1,j,1, j,1 µ P2,P 3,j,1, j,2 µ P0,P 2,j,2, and j,2 µ P1,P 3,j,2. The equations for the proliferating and clonogenic compartments are compactly written as dp i dt dc i dt = = [ { 4 } 4 1 α i (µ Pi,Ps + µ Pi,Cs P i + µ Ps,P i P s ]f + β i C i δ P,iP i N + j=1 k=1 [ α i P i + { 2 ( j,kκ Pi,j,k 4 j,k µ Pi,Ps,j,k P i (2.5 s=i i + j,k µ Ps,P i,j,kp s + γ Ci,P i,j,kc i }, 4 N µ Ps,C i P s ]f β i C i δ C,iC i j=1 k=1 2 j,k (κ Ci,j,k + γ Ci,P i,j,k C i, (2.6 where i I. The system of equations which represents the dynamics as illustrated in Figure 1 are given by (2.5 and (2.6, which are subject to the initial condition ( Discussion Ultimately, the majority of cells reside in the P 3 and C 3 compartments so that if any cytotoxic agent is administered the change in the number of cells is algebraic at best. This suggests that alternate treatment modes should be sought to reduce the drug resistant populations and the number of cancerous cells. Such treatment modalities as the use of surgery, radiotherapy, and 5
6 immunotherapies using cytokines, angio-genesis inhibitors, and anti-metastatic agents could be employed in a comprehensive treatment plan for the patient. The formulation of the cancer evolution and the subsequent treatment focuses on the heterogenous nature of the cancer and the effects drug resistance. Thus, this provides a system that can be utilized by clinicians to determine the effectiveness of treatment regimens employing multiple cytotoxic agents to predict the response of the cancer to a given strategy. Additionally, the model presents a framework in which alternate treatment strategies can be evaluated. A future direction is to solve numerically the optimal control problem for the treatment schedule in order to maximize the life expectancy and quality of life of the patient. Modeling the treatment of cancer has difficulties since a number of the underlying biological mechanisms are not clearly understood, for example, the development of resistance to a given treatment. Typically, tumors are not composed of a single strain of cancer cell but consist of several prominent strains, due to mutations, which will react differently to the various cytotoxic agents utilized for treatment. These mutations greatly complicate the model and need to be included for a better understanding of the effects of a given treatment plan. Future research directions include the addition of more realism in the model to account for mutations in the cancer cells and a more comprehensive treatment plan, including considerations of pharmacokinetics and toxicity of treatments, to include all possible modes, in particular radiotherapy and angiogenesis inhibitors, for combatting the cancer and retarding its development. Additionally, an optimal control problem needs to be developed, tailored to every patient, that determines the most effective treatment plan for the patient that accounts for the disease and the patients health and mental state. We believe that the use of a tailored individual comprehensive treatment plan using multimode treatments should lead to a better quality of life for the patient as well as a longer life expectancy. Acknowledgement: FBH was supported in part by the National Science Foundation Grant DMS References [1] D. C. Baquiran and J. Gallagher, Lippincott s Cancer Chemotherapy Handbook, Lippincott- Raven Publishers Philadelphia, [2] M. D. Cridland, Fundamentals of Cancer Chemotherapy, University Park Press Baltimore, [3] D. S. Fischer, M. T. Knobf, and H. J. Durivage, The Cancer Chemotherapy Handbook, 5th ed., Mosby St Louis, [4] J. J. Westman, B. R. Fabijonas, D. L. Kern, and F. B. Hanson, Compartmental Model for Cancer Evolution: Chemotherapy and Drug Resistance, Math. Biosci. (submitted
Compartmental Model for Cancer Evolution: Chemotherapy and Drug Resistance
Compartmental Model for Cancer Evolution: Chemotherapy and Drug Resistance Department of Mathematics, University of California, Box 951555, Los Angeles, CA 90095-1555, USA Department of Mathematics, Southern
More informationAnticancer Drugs. University of Sulaimani Faculty of Medical Sciences School of Pharmacy Pharmacology & Toxicology Dept.
University of Sulaimani Faculty of Medical Sciences School of Pharmacy Pharmacology & Toxicology Dept. Anticancer Drugs Prepared by: Hussein A. Muhammad MSc cancer Pharmacology hussein.al-barazanchi@kissr.edu.krd
More informationMathematics Meets Oncology
.. Mathematics Meets Oncology Mathematical Oncology Philippe B. Laval Kennesaw State University November 12, 2011 Philippe B. Laval (Kennesaw State University)Mathematics Meets Oncology November 12, 2011
More informationModeling Multi-Mutation And Drug Resistance: A Case of Immune-Suppression
Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 14, Number 6 (2018), pp. 787-807 Research India Publications http://www.ripublication.com/gjpam.htm Modeling Multi-Mutation And Drug
More informationMathematical Model Solid Tumor at the Stage of Angiogenesis with Immune Response
Mathematical Model Solid Tumor at the Stage of Angiogenesis with Immune esponse Deep Shikha Dixit, Deepak Kumar, Sanjeev Kr,ajesh Johri. Department of Mathematics, CET IILM, Gr. Noida.. Department of Mathematics,
More informationSimulation of the Spread of Epidemic Disease Using Persistent Surveillance Data
Excerpt from the Proceedings of the COMSOL Conference 2010 Boston Simulation of the Spread of Epidemic Disease Using Persistent Surveillance Data Yu Liang 1*, Zhenjun Shi 1, Subramania I. Sritharan 2 and
More informationModeling origin and natural evolution of low-grade gliomas
Modeling origin and natural evolution of low-grade gliomas Mathilde Badoual Paris Diderot University, IMNC lab 2nd HTE workshop: Mathematical & Computer Modeling to study tumors heterogeneity in its ecosystem,
More informationOptimal Delivery of Chemotherapeutic Agents in Cancer
16th European Symposium on Computer Aided Process Engineering and 9th International Symposium on Process Systems Engineering W. Marquardt, C. Pantelides (Editors) 2006 Published by Elsevier B.V. 1643 Optimal
More informationMODELLING INFECTIOUS DISEASES. Lorenzo Argante GSK Vaccines, Siena
MODELLING INFECTIOUS DISEASES Lorenzo Argante GSK Vaccines, Siena lorenzo.x.argante@gmail.com GSK IN A NUTSHELL GSK VACCINES - GLOBAL PRESENCE SIENA RESEARCH AND DEVELOPMENT (R&D) SITE EXPLORATORY DATA
More informationMATHEMATICAL MODELS OF THE ADAPTIVE IMMUNE RESPONSE IN A NOVEL CANCER IMMUNOTHERAPY
MATHEMATICAL MODELS OF THE ADAPTIVE IMMUNE RESPONSE IN A NOVEL CANCER IMMUNOTHERAPY by Bryan A. Dawkins A dissertation submitted to the faculty of The University of Central Oklahoma in partial fulfillment
More informationSummary of Evolution and the Requirements for the Specific Cure of Cancer
Summary of Evolution and the Requirements for the Specific Cure of Cancer The definition of cancer Cancer is defined by malignant behavior, (e.g. cell proliferation and invasiveness in an abnormal context.
More informationA mathematical model of tumor growth and its response to single irradiation
Watanabe et al. Theoretical Biology and Medical Modelling (2016) 13:6 DOI 10.1186/s12976-016-0032-7 RESEARCH Open Access A mathematical model of tumor growth and its response to single irradiation Yoichi
More informationBehavior-Disease Models with respect to HIV Dynamics
Behavior-Disease Models with respect to HIV Dynamics Aidan Grennell Western Carolina University 1 Abstract Expanding on the Susceptible-Infected-Recovered (SIR) epidemiological models, we review Towards
More informationThe roadmap. Why do we need mathematical models in infectious diseases. Impact of vaccination: direct and indirect effects
Mathematical Models in Infectious Diseases Epidemiology and Semi-Algebraic Methods Why do we need mathematical models in infectious diseases Why do we need mathematical models in infectious diseases Why
More informationStochastic modeling of carcinogenesis
Stochastic modeling of carcinogenesis Rafael Meza Department of Epidemiology University of Michigan SPH-II 5533 rmeza@umich.edu http://www.sph.umich.edu/faculty/rmeza.html Outline Multistage carcinogenesis
More informationarxiv: v1 [q-bio.to] 17 Apr 2016
Optimized Treatment Schedules for Chronic Myeloid Leukemia Qie He 1, Junfeng Zhu 1, David Dingli 2, Jasmine Foo 3**, Kevin Leder 2*, arxiv:1604.04913v1 [q-bio.to] 17 Apr 2016 1 Department of Industrial
More informationVIRUS POPULATION DYNAMICS
MCB 137 VIRUS DYNAMICS WINTER 2008 VIRUS POPULATION DYNAMICS Introduction: The basic epidemic model The classical model for epidemics is described in [1] and [Chapter 10 of 2]. Consider a population of
More informationA Model for the CD4 Cell Counts in an HIV/AIDS Patient and its Application in Treatment Interventions
American Journal of Infectious Diseases (): 6-65, 5 ISSN: 553-63 5 Science Publications A Model for the CD4 Cell Counts in an HIV/AIDS Patient and its Application in Treatment Interventions Richard O.
More informationModeling Imatinib-Treated Chronic Myeloid Leukemia
Modeling Imatinib-Treated Chronic Myeloid Leukemia Cara Peters cpeters3@math.umd.edu Advisor: Dr. Doron Levy dlevy@math.umd.edu Department of Mathematics Center for Scientific Computing and Mathematical
More informationStochastic and Numerical Modeling of HIV/AIDS. Spread in a Complex System and Its Application to. the HIV Cases in Indonesia
Applied Mathematical Sciences, Vol. 9, 2015, no. 122, 6095-6106 HIKAI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2015.59564 Stochastic and Numerical Modeling of HIV/AIDS Spread in a Complex System
More informationEpidemiological Model of HIV/AIDS with Demographic Consequences
Advances in Applied Mathematical Biosciences. ISSN 2248-9983 Volume 5, Number 1 (2014), pp. 65-74 International Research Publication House http://www.irphouse.com Epidemiological Model of HIV/AIDS with
More information"The standard treatment for almost all cancers is surgical removal of the lump."
Cancer Treatment As continuous improvements in our knowledge and new and evolving methods of treatment are developed, pet owners and their veterinarians have more options available when cancer is diagnosed.
More informationSEIQR-Network Model with Community Structure
SEIQR-Network Model with Community Structure S. ORANKITJAROEN, W. JUMPEN P. BOONKRONG, B. WIWATANAPATAPHEE Mahidol University Department of Mathematics, Faculty of Science Centre of Excellence in Mathematics
More informationNormal Cell Growth and Development
Normal Cell Growth and Development Noncancerous Versus Cancerous Tumors Cancerous Cell Growth and Development Cancer Genetics Causes of Cancer Epidemiology of Cancer Types of Cancer Resources Normal Cell
More informationMathematical modelling of spatio-temporal glioma evolution
Papadogiorgaki et al. Theoretical Biology and Medical Modelling 213, 1:47 RESEARCH Open Access Mathematical modelling of spatio-temporal glioma evolution Maria Papadogiorgaki 1*, Panagiotis Koliou 2, Xenofon
More informationMOGA-based Multi-drug Optimisation for Cancer Chemotherapy
MOGA-based Multi-drug Optimisation for Cancer Chemotherapy S Algoul, M S Alam*, K Sakib, M A Hossain and M A A Majumder University of Bradford, Bradford, UK, *University of Dhaka, Bangladesh {S.K.A.Algoul,k.muheymin-us-sakib;
More informationStructured models for dengue epidemiology
Structured models for dengue epidemiology submitted by Hannah Woodall for the degree of Doctor of Philosophy of the University of Bath Department of Mathematical Sciences September 24 COPYRIGHT Attention
More informationA Hormone Therapy Model for Breast Cancer Using Linear Cancer Networks
Rose-Hulman Undergraduate Mathematics Journal Volume 15 Issue 1 Article 9 A Hormone Therapy Model for Breast Cancer Using Linear Cancer Networks Michelle McDuffie Western Carolina University, mjmcduffie1@catamount.wcu.edu
More informationModeling Three-dimensional Invasive Solid Tumor Growth in Heterogeneous Microenvironment under Chemotherapy
Modeling Three-dimensional Invasive Solid Tumor Growth in Heterogeneous Microenvironment under Chemotherapy Hang Xie 1, Yang Jiao 2, Qihui Fan 3, Miaomiao Hai 1, Jiaen Yang 1, Zhijian Hu 1, Yue Yang 4,
More informationModeling of cancer virotherapy with recombinant measles viruses
Modeling of cancer virotherapy with recombinant measles viruses Thomas W. Carr Department of Mathematics Southern Methodist University Dallas, TX Collaborators: Krešimir Josić Dept. of Mathematics, University
More informationAppendix (unedited, as supplied by the authors)
Appendix (unedited, as supplied by the authors) Details of the mathematical model The model used for the simulations in this manuscript was adapted from a previously described model of HCV transmission
More informationChallenges in Synthesis of Optimal Controls For Problems Arising in Biomedicine
Challenges in Synthesis of Optimal Controls For Problems Arising in Biomedicine ITN SADCO meeting January 21-25, 2013, Funchal, Portugal Urszula Ledzewicz Dept. of Mathematics and Statistics Southern Illinois
More informationOptimizing Drug Regimens in Cancer Chemotherapy
Optimizing Drug Regimens in Cancer Chemotherapy A. ILIADIS, D. BARBOLOSI Department of Pharmacokinetics, Faculty of Pharmacy University of Méditerranée 27, bld. Jean Moulin, 13385 Marseilles Cedex 5 FRANCE
More informationTumour-Immune Interaction Model with Cell Cycle Effects Including G 0 Phase
MATEMATIKA, 2018, Special Issue, 33 44 c Penerbit UTM Press. All rights reserved Tumour-Immune Interaction Model with Cell Cycle Effects Including G 0 Phase 1 Nor Aziran Awang, 2 Normah Maan * and 3 Dasui
More informationMathematical Modeling of the Role of Survivin on Dedifferentiation and Radioresistance in Cancer
Mathematical Modeling of the Role of Survivin on Dedifferentiation and Radioresistance in Cancer Adam Rhodes, Thomas Hillen April 30, 2016 Centre for Mathematical Biology, University of Alberta, Canada
More informationThursday. Compartmental Disease Models
Thursday Compartmental Disease Models Model Formulation Major decisions in designing a model Even after compartmental framework is chosen, still need to decide: Deterministic vs stochastic Discrete vs
More informationOverview of Cancer. Mylene Freires Advanced Nurse Practitioner, Haematology
Overview of Cancer Mylene Freires Advanced Nurse Practitioner, Haematology Aim of the Presentation Review basic concepts of cancer Gain some understanding of the socio-economic impact of cancer Order of
More informationSIS-SEIQR Adaptive Network Model for Pandemic Influenza
SIS-SEIQR Adaptive Network Model for Pandemic Influenza WANNIKA JUMPEN,2, SOMSAK ORANKITJAROEN,2, PICHIT BOONKRONG,2 BOONMEE WATTANANON, BENCHAWAN WIWATANAPATAPHEE,2 Department of Mathematics, Faculty
More informationModeling of epidemic spreading with white Gaussian noise
Article Statistical Physics and Mathematics for Complex Systems December 20 Vol.56 No.34: 3683 3688 doi: 0.007/s434-0-4753-z SPECIAL TOPICS: Modeling of epidemic spreading with white Gaussian noise GU
More informationProject for Math. 224 DETECTION OF DIABETES
Project for Math. 224 DETECTION OF DIABETES Diabetes is a disease of metabolism which is characterized by too much sugar in the blood and urine. Because of the lack of insulin (a hormone), the patient
More informationUse of radiation to kill diseased cells. Cancer is the disease that is almost always treated when using radiation.
Radiation Therapy Use of radiation to kill diseased cells. Cancer is the disease that is almost always treated when using radiation. One person in three will develop some form of cancer in their lifetime.
More informationExercises on SIR Epidemic Modelling
Exercises on SIR Epidemic Modelling 1 Epidemic model (from Wikipedia) An epidemic model is a simplified means of describing the transmission of communicable disease through individuals. The modeling of
More informationMathematical Modeling of Treatment SIR Model with Respect to Variable Contact Rate
International Proceedings of Economics Development and Research IPEDR vol.83 (25) (25) IACSIT Press, Singapore Mathematical Modeling of Treatment SIR Model with Respect to Variable Contact Rate Paritosh
More informationSpreading of Epidemic Based on Human and Animal Mobility Pattern
Spreading of Epidemic Based on Human and Animal Mobility Pattern Yanqing Hu, Dan Luo, Xiaoke Xu, Zhangang Han, Zengru Di Department of Systems Science, Beijing Normal University 2009-12-22 Background &
More informationON ATTAINING MAXIMAL AND DURABLE SUPPRESSION OF THE VIRAL LOAD. Annah M. Jeffrey, Xiaohua Xia and Ian K. Craig
ON ATTAINING MAXIMAL AND DURABLE SUPPRESSION OF THE VIRAL LOAD Annah M. Jeffrey, Xiaohua Xia and Ian K. Craig Department of Electrical, Electronic and Computer Engineering, University of Pretoria, Pretoria
More informationCOMPETITIVE INTERFERENCE BETWEEN INFLUENZA VIRAL STRAINS
CANADIAN APPLIED MATHEMATICS QUARTERLY Volume 17, Number 2, Summer 2009 COMPETITIVE INTERFERENCE BETWEEN INFLUENZA VIRAL STRAINS SEYED M. MOGHADAS, CHRISTOPHER S. BOWMAN AND JULIEN ARINO ABSTRACT. We propose
More informationFigure S1. Standard curves for amino acid bioassays. (A) The standard curve for leucine concentration versus OD600 values for L. casei.
Figure S1. Standard curves for amino acid bioassays. (A) The standard curve for leucine concentration versus OD600 values for L. casei. (B) The standard curve for lysine concentrations versus OD600 values
More informationSummary Report for HIV Random Clinical Trial Conducted in
Summary Report for HIV Random Clinical Trial Conducted in 9-2014 H.T. Banks and Shuhua Hu Center for Research in Scientific Computation North Carolina State University Raleigh, NC 27695-8212 USA Eric Rosenberg
More informationA kinetic model of tumor growth and its radiation response with an application to Gamma Knife stereotactic radiosurgery
A kinetic model of tumor growth and its radiation response with an application to Gamma Knife stereotactic radiosurgery Yoichi Watanabe 1, Erik L. Dahlman 1, Kevin Z. Leder 2, and Susanta K. Hui 1 1 Department
More informationCANCER TREATMENT. Sent from the Diagnostic Imaging Atlas Page 1 of 5
CANCER TREATMENT When cancer is diagnosed in a pet continuous improvements in our knowledge and new and evolving methods of treatment give options to owners and their veterinarians. These notes are provided
More informationReduction of Mortality Rate Due to AIDS When Treatment Is Considered
Pure and Applied Mathematics Journal 216; 5(4): 97-12 http://www.sciencepublishinggroup.com/j/pamj doi: 1.11648/j.pamj.21654.12 ISSN: 2326-979 (Print); ISSN: 2326-9812 (Online) Reduction of Mortality Rate
More informationUNIVERSITY OF MEDICINE AND PHARMACY CRAIOVA PhD SCHOOL. PhD THESIS
UNIVERSITY OF MEDICINE AND PHARMACY CRAIOVA PhD SCHOOL PhD THESIS THE IMPORTANCE OF TUMOR ANGIOGENESIS IN CEREBRAL TUMOR DIAGNOSIS AND THERAPY ABSTRACT PhD COORDINATOR: Prof. univ. dr. DRICU Anica PhD
More informationSelection at one locus with many alleles, fertility selection, and sexual selection
Selection at one locus with many alleles, fertility selection, and sexual selection Introduction It s easy to extend the Hardy-Weinberg principle to multiple alleles at a single locus. In fact, we already
More informationGame theory and epidemiology
Game theory and epidemiology Biomathematics Seminar Fall 2016 Fan Bai Department of Mathematics and Statistics, Texas Tech University September 13, 2016 Outline Why apply game theory in vaccination? Theory
More informationMathematical Modeling for the Tumor Growth in the Bladder
IJISET - International Journal of Innovative Science, Engineering & Technology, Vol. 2 Issue 5, May 25. Mathematical Modeling for the Tumor Growth in the Bladder L. N. M. Tawfiq & S. A. Abdul-Jabbar Department
More informationarxiv: v2 [math.oc] 15 Nov 2016
Optimizing chemoradiotherapy to target multi-site metastatic disease and tumor growth arxiv:1603.00349v2 [math.oc] 15 Nov 2016 Hamidreza Badri, 1 Ehsan Salari, 2 Yoichi Watanabe, 3 Kevin Leder 1 1 Department
More informationUNIVERSITY OF CALIFORNIA SANTA CRUZ A STOCHASTIC DYNAMIC MODEL OF THE BEHAVIORAL ECOLOGY OF SOCIAL PLAY
. UNIVERSITY OF CALIFORNIA SANTA CRUZ A STOCHASTIC DYNAMIC MODEL OF THE BEHAVIORAL ECOLOGY OF SOCIAL PLAY A dissertation submitted in partial satisfaction of the requirements for the degree of BACHELOR
More informationSensitivity analysis for parameters important. for smallpox transmission
Sensitivity analysis for parameters important for smallpox transmission Group Members: Michael A. Jardini, Xiaosi Ma and Marvin O Ketch Abstract In order to determine the relative importance of model parameters
More informationNATURAL KILLER T CELLS EBOOK
08 April, 2018 NATURAL KILLER T CELLS EBOOK Document Filetype: PDF 90.41 KB 0 NATURAL KILLER T CELLS EBOOK Natural killer T cells (NK T cells) are a type of lymphocyte, or white blood cell. Natural killer
More informationThe Adaptive Immune Response. T-cells
The Adaptive Immune Response T-cells T Lymphocytes T lymphocytes develop from precursors in the thymus. Mature T cells are found in the blood, where they constitute 60% to 70% of lymphocytes, and in T-cell
More informationLinking Errors in Trend Estimation in Large-Scale Surveys: A Case Study
Research Report Linking Errors in Trend Estimation in Large-Scale Surveys: A Case Study Xueli Xu Matthias von Davier April 2010 ETS RR-10-10 Listening. Learning. Leading. Linking Errors in Trend Estimation
More informationResearch Article A Mathematical Model of Tumor Volume Changes during Radiotherapy
The Scientific World Journal Volume 203, Article ID 8070, 5 pages http://dx.doi.org/0.55/203/8070 Research Article A Mathematical Model of Tumor Volume Changes during Radiotherapy Ping Wang and Yuanming
More informationCOURSE: Medical Microbiology, PAMB 650/720 - Fall 2008 Lecture 16
COURSE: Medical Microbiology, PAMB 650/720 - Fall 2008 Lecture 16 Tumor Immunology M. Nagarkatti Teaching Objectives: Introduction to Cancer Immunology Know the antigens expressed by cancer cells Understand
More informationUNC-Duke Biology Course for Residents Fall
UNC-Duke Biology Course for Residents Fall 2018 1 UNC-Duke Biology Course for Residents Fall 2018 2 UNC-Duke Biology Course for Residents Fall 2018 3 UNC-Duke Biology Course for Residents Fall 2018 4 UNC-Duke
More informationDynamique des populations et résistance aux traitements : modèles mathématiques
Dynamique des populations et résistance aux traitements : modèles mathématiques Alexander Lorz 1 R. Chisholm, J. Clairambault, A. Escargueil, M.E. Hochberg, T. Lorenzi, P. Markowich, B. Perthame, E. Trélat
More informationStatistical Challenges in Immunotherapy: Non Proportional Hazard Model. BBS / PSI CIT event 15-June-2017, Basel Claude BERGE, Roche
Statistical Challenges in Immunotherapy: Non Proportional Hazard Model BBS / PSI CIT event 15-June-2017, Basel Claude BERGE, Roche 1 Statistical Challenges Biomarker Efficacy Endpoint Study Design & Analysis
More informationDesign for Targeted Therapies: Statistical Considerations
Design for Targeted Therapies: Statistical Considerations J. Jack Lee, Ph.D. Department of Biostatistics University of Texas M. D. Anderson Cancer Center Outline Premise General Review of Statistical Designs
More informationAppendix Figure S1 A B C D E F G H
ppendix Figure S1 C D E F G H ppendix Figure S1. RT and chemotherapy alter PD-L1 expression in PDC cells. Flow cytometric analysis of PD-L1 expression in () KPC and () Pan02 cells following treatment with
More informationA mathematical model for the primary tumor of mcrc
A mathematical model for the primary tumor of mcrc Marta Leocata Joint work with F.Flandoli, C. Ricci, M.C. Polito, V. De Mattei December 2, 2016 University of Pisa Plan of the talk General Project; A
More informationStochastic Modelling of the Spatial Spread of Influenza in Germany
Stochastic ling of the Spatial Spread of Influenza in Germany, Leonhard Held Department of Statistics Ludwig-Maximilians-University Munich Financial support by the German Research Foundation (DFG), SFB
More informationMathematical Modelling of Pulmonary and Extra-pulmonary Tuberculosis
Mathematical Modelling of Pulmonary and xtra-pulmonary Tuberculosis ita H. Shah # and Jyoti Gupta * # Professor, Department of Mathematics, Gujarat University, Ahmedabad, Gujarat, India, Research Scholar,
More information- is a common disease - 1 person in 3 can expect to contract cancer at some stage in their life -1 person in 5 can expect to die from it
MBB157 Dr D Mangnall The Molecular Basis of Disease CANCER Lecture 1 One of the simpler (and better) definitions of cancer comes from the American Cancer Society, who define cancer as; 'Cancer is a group
More informationSimulating the Tumor Growth with Cellular Automata Models
Simulating the Tumor Growth with Cellular Automata Models S. Zouhri Université Hassan II- Mohammédia, Faculté des Sciences Ben M'sik Département de Mathématiques, B.7955, Sidi Othmane, Casablanca, Maroc
More informationAddressing Breast Cancer's High Recurrence Rates: The Breast Cancer Translational Center of Excellence (TCE)
Transcript Details This is a transcript of an educational program accessible on the ReachMD network. Details about the program and additional media formats for the program are accessible by visiting: https://reachmd.com/programs/medical-breakthroughs-from-penn-medicine/addressing-breast-cancershigh-recurrence-rates-breast-cancer-translational-center-excellence-tce/7981/
More informationBayesian graphical models for combining multiple data sources, with applications in environmental epidemiology
Bayesian graphical models for combining multiple data sources, with applications in environmental epidemiology Sylvia Richardson 1 sylvia.richardson@imperial.co.uk Joint work with: Alexina Mason 1, Lawrence
More informationPersonalized medicine by the use of mathematical models for angiogenesis: validation in a Mesenchymal Chondrosarcoma patient
Personalized medicine by the use of mathematical models for angiogenesis: validation in a Mesenchymal Chondrosarcoma patient Agur Zvia Institute for Medical BioMathematics, IMBM Agenda Medical problem:
More informationKrunal Amin 7/17/2010 Josh Cannon Topics in Biology
SUMMER VENTURES UNC CHARLOTTE 2010 1 Malignant Melanoma Krunal Amin 7/17/2010 Josh Cannon Topics in Biology 2 Abstract Malignant melanoma is a cancer of melanocytes. It is caused by environmental (mainly
More informationMathematical Modeling of PDGF-Driven Glioblastoma Reveals Optimized Radiation Dosing Schedules
Mathematical Modeling of PDGF-Driven Glioblastoma Reveals Optimized Radiation Dosing Schedules Kevin Leder, Ken Pittner, Quincey LaPlant, Dolores Hambardzumyan, Brian D. Ross, Timothy A. Chan, Eric C.
More informationBiol403 MAP kinase signalling
Biol403 MAP kinase signalling The mitogen activated protein kinase (MAPK) pathway is a signalling cascade activated by a diverse range of effectors. The cascade regulates many cellular activities including
More informationA METAPOPULATION MODEL OF GRANULOMA FORMATION IN THE LUNG DURING INFECTION WITH MYCOBACTERIUM TUBERCULOSIS. Suman Ganguli.
MATHEMATICAL BIOSCIENCES http://www.mbejournal.org/ AND ENGINEERING Volume, Number 3, August 5 pp. 535 56 A METAPOPULATION MODEL OF GRANULOMA FORMATION IN THE LUNG DURING INFECTION WITH MYCOBACTERIUM TUBERCULOSIS
More informationA Game Theoretical Approach for Hospital Stockpile in Preparation for Pandemics
Proceedings of the 2008 Industrial Engineering Research Conference J. Fowler and S. Mason, eds. A Game Theoretical Approach for Hospital Stockpile in Preparation for Pandemics Po-Ching DeLaurentis School
More informationResponsiveness to feedback as a personal trait
Responsiveness to feedback as a personal trait Thomas Buser University of Amsterdam Leonie Gerhards University of Hamburg Joël van der Weele University of Amsterdam Pittsburgh, June 12, 2017 1 / 30 Feedback
More informationDeterministic Compartmental Models of Disease
Math 191T, Spring 2019 1 2 3 The SI Model The SIS Model The SIR Model 4 5 Basics Definition An infection is an invasion of one organism by a smaller organism (the infecting organism). Our focus is on microparasites:
More informationMMCS Turkey Flu Pandemic Project
MMCS Turkey Flu Pandemic Project This is a group project with 2 people per group. You can chose your own partner subject to the constraint that you must not work with the same person as in the banking
More informationAN ORDINARY DIFFERENTIAL EQUATION MODEL OF DIABETIC POPULATION IN NEW DELHI
Indian Journal of Mathematics and Mathematical Sciences Vol. 7, No. 1, (June 2011) : 45-50 AN ORDINARY DIFFERENTIAL EQUATION MODEL OF DIABETIC POPULATION IN NEW DELHI Sandhya, Deepak Kumar & Prerna Pandit
More informationIdentification of influential proteins in the classical retinoic acid signaling pathway
Ghaffari and Petzold Theoretical Biology and Medical Modelling (2018) 15:16 https://doi.org/10.1186/s12976-018-0088-7 RESEARCH Open Access Identification of influential proteins in the classical retinoic
More informationAgro/Ansc/Bio/Gene/Hort 305 Fall, 2017 MEDICAL GENETICS AND CANCER Chpt 24, Genetics by Brooker (lecture outline) #17
Agro/Ansc/Bio/Gene/Hort 305 Fall, 2017 MEDICAL GENETICS AND CANCER Chpt 24, Genetics by Brooker (lecture outline) #17 INTRODUCTION - Our genes underlie every aspect of human health, both in function and
More informationMATHEMATICAL STUDY OF BITING RATES OF MOSQUITOES IN TRANSMISSION OF DENGUE DISEASE
ORIGINAL RESEARCH ARTICLE OPEN ACCESS MATHEMATICAL STUDY OF BITING RATES OF MOSQUITOES IN TRANSMISSION OF DENGUE DISEASE *G. R. Phaijoo, D. B. Gurung Department of Natural Sciences (Mathematics), School
More informationA Monogenous MBO Approach to Satisfiability
A Monogenous MBO Approach to Satisfiability Hussein A. Abbass University of New South Wales, School of Computer Science, UC, ADFA Campus, Northcott Drive, Canberra ACT, 2600, Australia, h.abbass@adfa.edu.au
More informationMathematical models of tumor growth and radiation response
Mathematical models of tumor growth and radiation response Yoichi Watanabe, Ph.D. Department of Radiation Oncology University of Minnesota North Central Chapter of AAPM Meeting, Wisconsin Dells, WI April
More information= Λ μs βs I N, (1) (μ + d + r)i, (2)
Advanced Studies in Biology, Vol., 29, no. 8, 383-39 Mathematical Model of the Influenza A(HN) Infection K. Hattaf and N. Yousfi 2 Laboratory Analysis, Modeling and Simulation Department of Mathematics
More informationBY Mrs. K.SHAILAJA., M. PHARM., LECTURER DEPT OF PHARMACY PRACTICE, SRM COLLEGE OF PHARMACY
BY Mrs. K.SHAILAJA., M. PHARM., LECTURER DEPT OF PHARMACY PRACTICE, SRM COLLEGE OF PHARMACY Cancer is a group of more than 100 different diseases that are characterized by uncontrolled cellular growth,
More informationA Nonlinear ODE Model of Tumor Growth and Effect of Immunotherapy and Chemotherapy Treatment in Colorectal Cancer
A Nonlinear ODE Model of Tumor Growth and Effect of Immunotherapy and Chemotherapy Treatment in Colorectal Cancer Hannah Savage Lisette G. de Pillis, Advisor Ami Radunskaya, Reader May, 2010 Department
More informationSupplementary Appendix
Supplementary Appendix This appendix has been provided by the authors to give readers additional information about their work. Supplement to: Bredel M, Scholtens DM, Yadav AK, et al. NFKBIA deletion in
More informationDisorders of Cell Growth & Neoplasia
General Pathology VPM 152 Disorders of Cell Growth & Neoplasia Lecture 3 Rate of growth, local invasion, and metastasis. Molecular basis of cancer (normal cell-cycle and cellular proliferation). Enrique
More informationMathematics for Infectious Diseases; Deterministic Models: A Key
Manindra Kumar Srivastava *1 and Purnima Srivastava 2 ABSTRACT The occurrence of infectious diseases was the principle reason for the demise of the ancient India. The main infectious diseases were smallpox,
More informationAn Elementary Approach to Modeling Drug Resistance in Cancer
An Elementary Approach to Modeling Drug Resistance in Cancer Cristian Tomasetti 1 Doron Levy 1 December 17, 2009 Abstract Resistance to drugs has been an ongoing obstacle to a successful treatment of many
More informationPubH 7405: REGRESSION ANALYSIS
PubH 7405: REGRESSION ANALYSIS APLLICATIONS B: MORE BIOMEDICAL APPLICATIONS #. SMOKING & CANCERS There is strong association between lung cancer and smoking; this has been thoroughly investigated. A study
More information1 Principles of Chemotherapy
1 Principles of Chemotherapy Angela Houlston The history of the development of chemotherapy Chemotherapy is the term given to refer to any drug or chemical treatment used to treat any disease. Cytotoxic
More informationModelling the risk of dengue for tourists in Rio de Janeiro, during. Janeiro, during the FIFA confederation cup in Brazil 2013
Modelling the risk of dengue for tourists in Rio de Janeiro, during the FIFA confederation cup in Brazil 2013 Raphael Ximenes, Eduardo Massad University of São Paulo November, 2013 Mathematical modeling
More information